Question

y' = x + y

Answer 1

y'-y=x

multiply everything by e^-x

y' e^(-x) - y e^(-x)= x

see that it is a product rule

Answer 2

(y e^(-x) )' = x e^-x

so integrate both sides

Answer 3

or you can save all the trouble and try case

y=x --> y'=1

y=x+1 --> y'=1 (y'+x=y)

y=-x-1 --> y'=-1 --> y+x= -1=y'